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प्रश्न
`((4x-3)/(2x+1))-10((2x+1)/(4x-3))=3,x≠-1/2,3/4`
उत्तर
`((4x-3)/(2x+1))-10((2x+1)/(4x-3))=3`
Putting `(4x-3)/(2x+1)=y`, We get:
`y-10/y=3`
⇒`(y^2-10)/y=3`
⇒`y^2-10=3y` [On cross multiplying]
⇒`y^2-3y-10=0`
⇒`y^2-(5-2)y-10=0`
⇒`y^2-5y+2y-10=0`
⇒`y(y-5)+2(y-5)=0`
⇒`(y-5)(y+2)=0`
⇒`y-5=0 or y+2=0`
⇒`y=5 or y=-2`
Case I :
If y=5, We get:
`(4x-3)/(2x+1)=5`
⇒` 4x-3=5(2x+1)` [On cross multiplying]
⇒`4x-3=10x+5 `
⇒`-6x=8`
⇒`-6x=8`
⇒`x=8/6`
⇒`x=-4/3`
Case II
If y=-2, We get :
`(4x-3)/(2x+1)=2`
⇒`4x-3=-2(2x+1)`
⇒`4x-3=-4x-2`
⇒`8x=1`
⇒` x=1/8`
Hence, the roots of the equation are `-4/3` and `1/8`
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